Jordan derivations and antiderivations on triangular matrices

被引：74

作者：

Benkovic, D ^{[1
]}

机构：

[1] Univ Maribor, Maribor 2000, Slovenia

来源：

LINEAR ALGEBRA AND ITS APPLICATIONS | 2005年 / 397卷

关键词：

triangular matrix algebra; Jordan derivation; antiderivation;

D O I：

10.1016/j.laa.2004.10.017

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We define an antiderivation from an algebra A into an A-imodule M as a linear map delta : A --> M such that delta(ab) = delta(b)a + bdelta(a) for all a, b is an element of A. The main result states that every Jordan derivation from the algebra of all upper triangular matrices into its bimodule is the sum of a derivation and an antiderivation. (C) 2004 Elsevier Inc. All rights reserved.

引用

收藏

页码：235 / 244

页数：10

相关论文

共 10 条

[1] Jordan isomorphisms of triangular matrix algebras over a connected commutative ring [J].

Beidar, KI ;

Bresar, M ;

Chebotar, MA .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2000, 312 (1-3) :197-201

[2] JORDAN MAPPINGS OF SEMIPRIME RINGS [J].

BRESAR, M .

JOURNAL OF ALGEBRA, 1989, 127 (01) :218-228

[3] CHARACTERIZATIONS OF DERIVATIONS ON SOME NORMED ALGEBRAS WITH INVOLUTION [J].

BRESAR, M .

JOURNAL OF ALGEBRA, 1992, 152 (02) :454-462

[4] Linear preservers on upper triangular operator matrix algebras [J].

Cui, JL ;

Hou, JC ;

Li, BR .

LINEAR ALGEBRA AND ITS APPLICATIONS, 2001, 336 :29-50

[5] JORDAN DERIVATIONS ON RINGS [J].

CUSACK, JM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 53 (02) :321-324

[6]

Herstein I.N., 1957, P AM MATH SOC, V8, P1104, DOI [10.2307/2032688, 10.1090/S0002-9939-1957-0095864-2, DOI 10.1090/S0002-9939-1957-0095864-2]

[7] Symmetric amenability and the nonexistence of Lie and Jordan derivations [J].

Johnson, BE .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1996, 120 :455-473

[8]

Molnar L., 1998, LINEAR MULTILINEAR A, V45, P189

[9] JORDAN HOMOMORPHISMS AND DERIVATIONS ON SEMISIMPLE BANACH ALGEBRAS [J].

SINCLAIR, AM .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1970, 24 (01) :209-&

[10]

Tang XM, 2001, LINEAR ALGEBRA APPL, V338, P145